I wouldn't even entertain the adhesive idea.

1. These racks are exposed to constant dynamic loading....bounce, bounce, etc. and would really test your adhesive of choice.
Mechanical fasteners rule for this app.

2. The new, deluxe canopies are very expensive and who wants to go hacking into that nice headliner that you paid dearly for, just to get to a gluing surface that may or may not work.

DD has a point, Dave.

I can send you some adhesive that would glue that white rack to the carpet/liner, and the carpet would leave the canopy shell before the rack would come unstuck from the carpet/liner..................but that could be a problem in that you're never going to be able to "unglue" it.

Thanks for all the input. I think I'm gonna go with the cedar 1X3 with the plastic rack screwed to it. I think I can do a tight fit force with the 1X3 so it will stay put. If not, i will get some of the glue Dan recommends.

Take your time with the chopsaw, and keep nipping until you get just the tightness that you want.
Put a bend in the 1x as you move it into place and then compression will take over when you let go.
Put the pre-drilled-to-the-cedar, plastic rack on the 1x after the 1x is in place.

Good luck.
Take pics.

Edit:
If you have metal framed windows it may be possible to use a piece of light aluminum angle (hardware store) that borrows some existing frame screws to join the 1x to the frame. It could be made tidy and would positively secure the 1x if compression didn't work.

In our Suburban
Cargo brace made for pick-up bed, cheap n easy...

That looks pretty damn nice Rog !

Holds 11 rod, 10'6" rods tap on the front windshield, other than that it's overhead n outta the way

That's the name of the game.
Up and outa the way.
Outa sight as well.

Nicely done.